When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found that it grew by $26$ centimeters each year. $4.5$ years after he moved into the house, the tree was $292$ centimeters tall. How tall was the tree when Vlad moved into the house?
Explanation: The tree grew by $26$ centimeters each year, so it grew by $26T$ centimeters in $T$ years. The tree's height at a given time is found by taking its height when Vlad moved to his new home and adding to it the length it grew since then. We can express this with the equation $H=A+26T$, where: $H$ represents the tree's height at a given time (in centimeters) $A$ represents the tree's original height (in centimeters) $T$ represents the time (in years) We want to find $A$, so let's first solve the equation for $A$ : $ \begin{aligned}H&=A+26T\\ A&=H-26T\end{aligned}$ Now, we know that after $4.5$ years $(T={4.5})$, the tree was $292$ centimeters tall $(H={292})$. Let's plug these values into the equation to find the value of $A$. $ A={292}-26\cdot{4.5}=175$ Therefore, when Vlad moved into the house, the tree was $175$ centimeters tall. To find how long it took the tree to reach a height of $357$ centimeters, we can plug $H=357$ into the equation and solve for $T$. $ \begin{aligned}175&=357-26T\\ 26T&=182\\ T&=7\end{aligned}$ When Vlad moved into the house, the tree was $175$ centimeters tall. The tree reached a height of $357$ centimeters $7$ years after Vlad moved in.